a.Convert complex number z=-1+/3i to a polar form z=r(cos(0)+isin(0)) b.Use a polar form of the number and De Moivre's Theorem to find z^9 Convert your answer back to z=a+bi form.

Q: Use the identity cos 20 = cos² 0 – sin² 0 to find a polar equation of the hyperbola x² – y² = 1.

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Q: (a) For complex numbers z₁ = 6 + 6j and z₂ = 4 − 4j, π (i) find z = 21. Present your result in polar…

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Q: Write the complex number z =(-1+3i) in polar form: z = T(cos 0+isin 0) where and 0 The angle should…

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Q: 1- Represent the following complex numbers in polar coordinate Z= 2 + 5j Y= -3 - 3j

A: Z=2+5j compare the complex number with z=a+bj a=2b=5 find the modulus r  r=a2+b2=22+52=4+25=29…

Q: -4/2 – 4V2i Express the complex number z = in polar formr cis 0.

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Q: Consider the complex numbers: z = 2 – i and w = 1+3i . Sketch (in the same diagram) 2, w, zw and z:

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Q: Q4) a) Find the polar form and represent graphically the complex number 7-5j b) Express…

A: We have to find Polar Form of Complex Number 7-5j We have to express 3cos232°+jsin232° in…

Q: Find all the roots in the complex plane using De Moivre's Formula in polar form and rectangular…

A: To find the fourth roots of -1 the De Moivre's formula convert the rectangular co-ordinate to polar…

Q: (a) Use the formula zk = Vr(co e+ 27tk cos +i sin 0+277K to find the indicated roots of the complex…

A: Given Z=-322(-1+i) Zk=rncosθ+2πkn+sinθ+2πkn, 0≤θ<2π The trigonometric form of the complex number…

Q: Put the following complex number 1 3 3 3 into polar form. Choose the correct answer from the…

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Q: Find the quotient z1/z2 of the complex numbers z1 = 12(cos 3π/4 + i sin3π/4) and z2 = 4(cos π/4 + i…

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Q: 1. Use the help of the polar representations of complex numbers to express (1+i)3 in the form a +…

A: As per bartleby guidelines only first three subparts are to be solved. Please upload other parts…

Q: Convert the given complex numbers to the required equivalent form: 1. 62 + j25 into polar form Ans.…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: 1. Use De Moivre's Theorem to write the following complex number -6 Z = (-1+i)30 in Polar Form z =…

A: The complex number z=-6(-1+i)30

Q: 3 What are the solutions to x³ = -2 – 2i in polar form?

A: The complex number is x3 = - 2 -2i

Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1– j2) 2 - j3 j 1+ j2…

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Q: If the complex number z = x + iy satisfies the condition |3z - 6i| = 3, then z lies on a. Circle…

A: We know that z=x+iy and z = x2+y2 Then 3z-6i = 33(x+iy)-6i = 33x+3iy-6i = 33x+(3y-6)i =…

Q: 1. Use the help of the polar representations of complex numbers to express (1+i)3 in the form a +…

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Q: Express the complex number z = 4 – 4/3i in polar form r(cos 0 + i sin 0). Select the correct answer…

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Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1 – j2), j 2- j3 1 +…

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Q: IV-1 Find the roots of the following complex numbers in polar form, correct to 3 decimal places. [4…

A: Thanks for the question :)And your upvote will be really appreciable ;) Correct Option :- C

Q: 7. Rewrite the complex number 4 + 7i into polar re" form.

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Q: Write the complex number z = (1+ v3 i)" in polar form: z = r(cos 0+ i sin 0) where

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Q: 11a Express the complex number z 10 cis in 6. rectangular form a + bi.

A: Given problem is :

Q: (a) Express the given complex number in to Polar Form (i) z= 1+ i

A: NOTE: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: (15) For the complex number z = ti find z2 by a) directly multiplying in the rectangular form given,…

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Q: 1. Consider the complex number z = -2(1 + i). (a) Compute z' by multiplying z by itself three times.…

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Q: b) Given the complex number z = -V32 + V32i. i. Express z in polar form. Vz and sketch ii. Obtain…

A: ----------------------------------------------------- Given: z = -32 + 32iAim: To express 'z' in…

Q: 2. Find the Cartesian (x+iy) form of this complex number 3π 3π Z=4(cos + 2 isin 377)

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Q: Transform z =2- 4i into trigonometric, polar, and exponential form. %3D

A: Topic:- complex number

Q: 2. Represent z = 3 – 3i in polar form.

A: As we know that; The polar form for the complex number z=x+iy is: z=rcosθ+isinθ  .....(1) Where;…

Q: Convert complex number z=-1+/3i to a polar form z=r(cos(0)+isin(0))

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Q: Find the four fourth complex roots of z = – 256. Express your answer in polar form and then convert…

A: So,

Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1- j2) j 2-j3 1+ j2…

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Q: Express the complex no v3 + i in polar form. Also show it by Argand diagram

A: Given that z=3+i convert the given complex number into polar form  also draw the Armand diagram

Q: Express the complex number z » -4 in polar formr cis ở. Select the correct answer below Hcs27

A: Given complex number can be written as Now, we know that, Therefore, we have

Q: Express the complex number z = - 1 - (square root 3)i in polar form: Z = r ( cos ( θ ) + i sin ( θ )…

A: Explained below

Q: Express the complex number z = -12i in polar form r cis 0. Select the correct answer below: O 6 cis…

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Q: ) Find the Cartesian form (i.e. æ + jy where x, y E R) for the complex number 1 (2+ j)(1 – 2j)´ - )…

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Q: - find polar form of the complex number z = (2√3-4i) + (-√3+51)..

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Q: Q3 Put the complex number Z = 18 + 26i in the "polar" form Z = rele where r, 0 ER and both r and 0…

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Q: The polar form of complex number (z=3+3i) is O 3 (cos 45+ i sin 45) √2 (cos 45 + i sin 45) O 31/2…

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Q: T Convert the complex number, z = 4( cos| + i sin from polar to rectangular form. Enter your answer…

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Q: Find the quotient of z1 = -6+2i and z2 = 7+8i in polar form %3D %3D

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Q: Express the complex number z = -V2 - V2i in polar form r(cos 0+i sin 0). Select the correct answer…

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Q: 2.1 Given the complex number z=3-j. 2.1.1 Show z on an Argand diagram. 2.1.2 Rewrite z in polar…

A: As per guidelines we are supposed to solve the maximum first question at a time. kindly post another…

Q: Find all the roots in the complex plane using De Moivre's Formula in polar form and rectangular…

A: Given the complex number 18 in polar form and rectangular form.

Q: =(-1= v3i)³

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Q: Find all the roots in the complex plane using De Moivre's Formula in polar form and rectangular…

A: To convert the complex number 1-j2 in polar form, substitute 1 for a and -2 for b in the formula…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.